Quantum phase transition in a frustrated two-dimensional magnetic system: A matrix projection approach

A matrix projection formalism is developed for the description of a frustrated two-dimensional antiferromagnet. This approach keeps safe all the advantages of the spherically symmetric self-consistent treatment (it strictly meets the spin constraint and the Mermin—Wagner theorem) but does not have its disadvantages. In particular, even in its simplest implementation, this approach provides a good agreement with the numerical simulations for two best-studied reference points: the zero frustration point and the point of a transition from the antiferromagnetic ordered phase to the disordered phase.